1. Data Generation
1-1. First cell type
p <- 8
first_n <- 150
corpula_mean_first <- c(10, 0, 10, 0, 10, 0, 10, 0) # mu
cov_mat_first <- matrix(0, p, p);
diag(cov_mat_first) <- c(20, 5, 20, 10, 20, 5, 20, 5)
cov_mat_first[1,5] <- 10; cov_mat_first[5,1] <- 10;
cov_mat_first[1,7] <- 10; cov_mat_first[7,1] <- 10;
cov_mat_first[4,5] <- 3; cov_mat_first[5,4] <- 3;
cov_mat_first[4,7] <- 3; cov_mat_first[7,4] <- 3;
norm_first <- MASS::mvrnorm(first_n, corpula_mean_first, cov_mat_first)
corpula_first <- norm_first
# nonparanormal transform
corpula_first <- apply(corpula_first, 2, function(x) {0.4 * sign(x) * abs(x)^1.6})
# this is the gaussian data we need to make nonparanormals
pairs(norm_first, asp = T, pch = 16, col = rgb(0.5,0.5,0.5,0.5), lower.panel = NULL)
# this is the nonparanormal
pairs(corpula_first, asp = T, pch = 16, col = rgb(0.5,0.5,0.5,0.5), lower.panel = NULL)
1-2. Second cell type
second_n <- 200
corpula_mean_second <- c(0, 10, 0, 10,
0, 10, 0, 10) # mu
cov_mat_second <- matrix(0, p, p)
diag(cov_mat_second) <- c(5, 20, 5, 10, 5, 20, 5, 20) # Sigma
cov_mat_second[1,5] <- 5; cov_mat_second[5,1] <- 2;
cov_mat_second[1,7] <- 5; cov_mat_second[7,1] <- 2;
norm_second <- MASS::mvrnorm(second_n, corpula_mean_second, cov_mat_second)
corpula_second <- norm_second
# nonparanormal transform
corpula_second <- apply(corpula_second, 2, function(x) {0.4 * sign(x) * abs(x)^1.6})
# this is the gaussian data we need to make nonparanormals
pairs(norm_second, asp = T, pch = 16, col = rgb(0.5,0.5,0.5,0.5), lower.panel = NULL)
# this is the nonparanormal
pairs(corpula_second, asp = T, pch = 16, col = rgb(0.5,0.5,0.5,0.5), lower.panel = NULL)
1-3. Third cell type
third_n <- 150
corpula_mean_third <- c(10, 0, 0, 10,
8, 8, 10, 10)
cov_mat_third <- matrix(4, p, p);
diag(cov_mat_third) <- c(5, 10, 5, 10, 5, 10, 5, 10) # Sigma
cov_mat_third[4,5] <- 5; cov_mat_third[5,4] <- 5;
#(1,3), (1,5), (1,7), (2,4), (2,6), (2,8), (3,5), (3,7), (4,6), (4,8), (5,7), (6,8)
norm_third <- MASS::mvrnorm(third_n, corpula_mean_third, cov_mat_third)
corpula_third <- norm_third
# nonparanormal transform
corpula_third <- apply(corpula_third, 2, function(x) {0.6 * sign(x) * abs(x)^1.8})
norm_expr <- MASS::mvrnorm(third_n, corpula_mean_third, cov_mat_third)
# this is the gaussian data we need to make nonparanormals
pairs(norm_third, asp = T, pch = 16, col = rgb(0.5,0.5,0.5,0.5), upper.panel = NULL)
# this is the nonparanormal
pairs(corpula_third, asp = T, pch = 16, col = rgb(0.5,0.5,0.5,0.5), upper.panel = NULL)
1-4. Combine the three cell types
full_dat <- rbind(cbind(corpula_first, rep(1, first_n)),
cbind(corpula_second, rep(2, second_n)),
cbind(corpula_third, rep(3, third_n)))
gen_dat <- full_dat[, 1:8]
gen_label <- full_dat[, 9]
pairs(gen_dat, asp = T, pch = 16, col = gen_label, lower.panel = NULL)
pairs(gen_dat, asp = T, pch = 16, col = rgb(0.5, 0.5, 0.5, 0.5), lower.panel = NULL)
1-5. 2 x 2 Example
set.seed(10)
n <- 500
mean_vec_1 <- c(20,0)
cov_mat_1 <- matrix(c(100, 0,
0, 50), 2, 2)
####
mean_vec_2 <- c(0,20)
cov_mat_2 <- matrix(c(50, 0,
0, 100), 2, 2)
dat_1 <- MASS::mvrnorm(n, mu = mean_vec_1, Sigma = cov_mat_1)
dat_2 <- MASS::mvrnorm(n, mu = mean_vec_2, Sigma = cov_mat_2)
dat <- rbind(dat_1, dat_2)
# dat_3 <- MASS::mvrnorm(n, mu = c(0,0), Sigma = diag(2))
# dat <- rbind(dat_1, dat_2, dat_3)
# par(mar = c(0.5, 0.5, 0.5, 0.5))
plot(dat[,1], dat[,2], asp = T,
pch = 16, col = rgb(0.5, 0.5, 0.5, 0.1))
dat_1 <- apply(dat_1, 2, function(x){x^2}) # copula-part (monotonic transformation)
dat_2 <- apply(dat_2, 2, function(x){x^2})
dat <- rbind(dat_1, dat_2)
plot(dat[,1], dat[,2], asp = T,
pch = 16, col = rgb(0.5, 0.5, 0.5, 0.1))
1-5. Defining functions for next section
- Define functions that calculate correlation matrices and draw heatmaps of corresponding matrices
library(reshape2) # melt function
library(ggplot2) # ggplot function
library(pcaPP) # Fast Kendall function
library(energy) # Distance Correlation
library(Hmisc) # Hoeffding's D measure
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
##
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
##
## format.pval, units
library(entropy) # Mutual Information
library(minerva) # Maximum Information Coefficient
library(XICOR) # Chatterjee's Coefficient
library(dHSIC) # Hilbert Schmidt Independence Criterion
library(VineCopula) # Blomqvist's Beta
make_cormat <- function(dat_mat){
matrix_dat <- matrix(nrow = ncol(dat_mat), ncol = ncol(dat_mat))
cor_mat_list <- list()
basic_cor <- c("pearson", "spearman")
# find each of the correlation matrices with Pearson, Spearman, Kendall Correlation Coefficients
for (i in 1:2){
cor_mat <- stats::cor(dat_mat, method = basic_cor[i])
cor_mat[upper.tri(cor_mat, diag = T)] <- NA
cor_mat_list[[i]] <- cor_mat
}
# functions that take matrix or data.frame as input
no_loop_function <- c(pcaPP::cor.fk, Hmisc::hoeffd,
minerva::mine, VineCopula::BetaMatrix)
for (i in 3:6){
fun <- no_loop_function[[i-2]]
cor_mat <- fun(dat_mat)
if (i == 4){ # Hoeffding's D
cor_mat <- cor_mat$D
} else if (i == 5){ # MIC
cor_mat <- cor_mat$MIC
}
cor_mat[upper.tri(cor_mat, diag = T)] <- NA
cor_mat_list[[i]] <- cor_mat
}
# functions that take two variables as input to calculate correlations.
need_loop <- c(energy::dcor2d, entropy::discretize2d,
XICOR::calculateXI, dHSIC::dhsic)
for (i in 7:10){
fun <- need_loop[[i-6]]
cor_mat <- matrix(nrow = ncol(dat_mat),
ncol = ncol(dat_mat))
for (j in 2:ncol(dat_mat)){
for (k in 1:(j-1)){
if (i == 8){ # Mutual Information
cor_mat[j, k] <- mi.empirical(fun(as.matrix(dat_mat[, j]),
as.matrix(dat_mat[, k]),
numBins1 = 20,
numBins2 = 20))
} else if (i == 10){ # HSIC
cor_mat[j, k] <- fun(as.numeric(dat_mat[, j]),
as.numeric(dat_mat[, k]))$dHSIC
} else {
cor_mat[j, k] <- fun(as.numeric(dat_mat[, j]),
as.numeric(dat_mat[, k]))
}
}
}
cor_mat[upper.tri(cor_mat, diag = T)] <- NA
cor_mat_list[[i]] <- cor_mat
}
return(cor_mat_list)
}
draw_heatmap <- function(cor_mat){
len <- 8
melted_cormat <- melt(cor_mat)
melted_cormat <- melted_cormat[!is.na(melted_cormat$value),]
break_vec <- round(as.numeric(quantile(melted_cormat$value,
probs = seq(0, 1, length.out = len),
na.rm = T)),
3)
break_vec[1] <- break_vec[1]-1
break_vec[len] <- break_vec[len]+1
melted_cormat$value <- cut(melted_cormat$value, breaks = break_vec)
heatmap_color <- unique(melted_cormat$value)
heatmap <- ggplot(data = melted_cormat, aes(x = Var2, y = Var1, fill = value))+
geom_tile(colour = "Black") +
ggplot2::scale_fill_manual(breaks = sort(heatmap_color),
values = rev(scales::viridis_pal(begin = 0, end = 1)
(length(heatmap_color)))) +
theme_bw() + # make the background white
theme(panel.border = element_blank(), panel.grid.major = element_blank(),
panel.grid.minor = element_blank(), axis.ticks = element_blank(),
# erase tick marks and labels
axis.text.x = element_blank(), axis.text.y = element_blank())
return (heatmap)
}
make_cor_heatmap <- function(dat_mat){
fun_lable <- c("Pearson's Correlation", "Spearman's Correlation", "Kendall's Correlation",
"Hoeffding's D", "MIC", "Blomqvist's Beta", "Distance Correlation",
"Mutual Information", "XI Correlation", "HSIC")
cor_heatmap_list <- list()
cor_abs_heatmap_list <- list()
# make correlation matrices
cor_mat_list <- make_cormat(dat_mat)
for (i in 1:10){
cor_mat <- cor_mat_list[[i]]
# get heatmaps
cor_heatmap <- draw_heatmap(cor_mat)
# ggplot labels
ggplot_labs <- labs(title = paste("Heatmap of", fun_lable[i]),
x = "",
y = "",
fill = "Coefficient") # change the title and legend label
cor_heatmap_list[[i]] <- cor_heatmap + ggplot_labs
if (i %in% c(1,2,3,4,6)){
cor_abs_mat <- abs(cor_mat_list[[i]])
cor_abs_heatmap <- draw_heatmap(cor_abs_mat)
ggplot_abs_labs <- labs(title = paste("Abs Heatmap of", fun_lable[i]),
x = "", # change the title and legend label
y = "",
fill = "Coefficient")
cor_abs_heatmap_list[[i]] <- cor_abs_heatmap + ggplot_abs_labs
} else {
ggplot_abs_labs <- labs(title = paste("Abs Heatmap of", fun_lable[i]),
subtitle = "Equivalent to Non-Abs Heatmap",
x = "", # change the title and legend label
y = "",
fill = "Coefficient")
cor_abs_heatmap_list[[i]] <- cor_heatmap + ggplot_abs_labs
}
}
ans <- list(cor_heatmap_list, cor_abs_heatmap_list)
return (ans)
}
lst <- make_cor_heatmap(gen_dat)
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lst2 <- lst[[2]]
# lst[[1]]
lst[[1]][[4]]
2. Dependence Measures
2-1. Pearson’s correlation coefficient (Linearity)
cor_pearson_mat <- stats::cor(gen_dat, method = "pearson")
cor_pearson_mat[upper.tri(cor_pearson_mat, diag = T)] <- NA
cor_pearson_mat[1:5,1:5]
## [,1] [,2] [,3] [,4] [,5]
## [1,] NA NA NA NA NA
## [2,] -0.51124056 NA NA NA NA
## [3,] 0.04030216 -0.26420526 NA NA NA
## [4,] 0.54492453 -0.03760496 -0.4081596 NA NA
## [5,] 0.87182314 -0.50282260 0.1475356 0.4792472 NA
# plot the correlations
cor_pearson_vec <- sort(abs(cor_pearson_mat), decreasing = T)
plot(cor_pearson_vec)
2-2. Spearman’s correlation coefficient (Monotone)
cor_spearman_mat <- stats::cor(gen_dat, method = "spearman")
cor_spearman_mat[upper.tri(cor_spearman_mat, diag = T)] <- NA
cor_spearman_mat[1:5,1:5]
## [,1] [,2] [,3] [,4] [,5]
## [1,] NA NA NA NA NA
## [2,] -0.5965524 NA NA NA NA
## [3,] 0.2178163 -0.2251929 NA NA NA
## [4,] 0.2366353 0.1471883 -0.4697439 NA NA
## [5,] 0.8719303 -0.5771796 0.3146677 0.1929999 NA
# plot the correlations
cor_spearman_vec <- sort(abs(cor_spearman_mat), decreasing = T)
plot(cor_spearman_vec)
2-3. Kendall’s correlation coefficient, τ (Monotone)
cor_kendall_mat <- stats::cor(gen_dat, method = "kendall")
cor_kendall_mat[upper.tri(cor_kendall_mat, diag = T)] <- NA
cor_kendall_mat[1:5,1:5]
## [,1] [,2] [,3] [,4] [,5]
## [1,] NA NA NA NA NA
## [2,] -0.3900922 NA NA NA NA
## [3,] 0.1431824 -0.16294990 NA NA NA
## [4,] 0.1318798 0.09976754 -0.3021723 NA NA
## [5,] 0.6769539 -0.37232866 0.1951583 0.1257555 NA
# plot the correlations
cor_kendall_vec <- sort(abs(cor_kendall_mat), decreasing = T)
plot(cor_kendall_vec)
2-4. Distance correlation (Non-linear)
library(energy)
cor_dist_mat <- matrix(nrow = ncol(gen_dat), ncol = ncol(gen_dat))
for (i in 2:ncol(gen_dat)){
for (j in 1:(i-1)){
cor_dist_mat[i,j] <- dcor2d(as.numeric(gen_dat[, i]), as.numeric(gen_dat[, j]))
}
}
cor_dist_mat[upper.tri(cor_dist_mat, diag = T)] <- NA
cor_dist_mat[1:5,1:5]
## [,1] [,2] [,3] [,4] [,5]
## [1,] NA NA NA NA NA
## [2,] 0.37063906 NA NA NA NA
## [3,] 0.05632691 0.14211149 NA NA NA
## [4,] 0.31254983 0.07329706 0.29714147 NA NA
## [5,] 0.74071342 0.37139492 0.07041593 0.2453794 NA
cor_dist_vec <- sort(abs(cor_dist_mat), decreasing = T)
plot(cor_dist_vec)
2-5. Hoeffding’s D measure (Distance)
library(Hmisc)
hoeff_dist <- hoeffd(x = as.matrix(gen_dat))
cor_hoeffd_mat <- hoeff_dist$D
cor_hoeffd_mat[upper.tri(cor_hoeffd_mat, diag = T)] <- NA
cor_hoeffd_vec <- sort(abs(cor_hoeffd_mat), decreasing = T)
plot(cor_hoeffd_vec)
2-6. Mutual information (MI) (information)
library(entropy)
cor_MI_mat <- matrix(nrow = ncol(gen_dat), ncol = ncol(gen_dat))
for (i in 2:ncol(gen_dat)){
for (j in 1:(i-1)){
y2d <- discretize2d(as.matrix(gen_dat[, i]),
as.matrix(gen_dat[, j]),
numBins1 = 20,
numBins2 = 20)
cor_MI_mat[i,j] <- as.numeric(mi.empirical(y2d))
}
}
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cor_MI_vec <- sort(abs(cor_MI_mat), decreasing = T)
plot(cor_MI_vec)
2-8. Chatterjee’s method
library(XICOR)
cor_XI_mat <- matrix(nrow = ncol(gen_dat), ncol = ncol(gen_dat))
for (i in 2:ncol(gen_dat)){
for (j in 1:(i-1)){
cor_XI_mat[i,j] <- calculateXI(as.numeric(gen_dat[, i]), as.numeric(gen_dat[, j]))
}
}
cor_XI_mat[upper.tri(cor_XI_mat, diag = T)] <- NA
cor_XI_vec <- sort(abs(cor_XI_mat), decreasing = T)
plot(cor_XI_vec)
2-9. Hilbert Schmidt Independence Criterion (HSIC)
- Disregard this coefficient
library(dHSIC)
cor_HSIC_mat <- matrix(nrow = ncol(gen_dat), ncol = ncol(gen_dat))
for (i in 2:ncol(gen_dat)){
for (j in 1:(i-1)){
cor_HSIC_mat[i,j] <- dhsic(as.numeric(gen_dat[, i]),
as.numeric(gen_dat[, j]))$dHSIC
}
}
cor_HSIC_mat[upper.tri(cor_HSIC_mat, diag = T)] <- NA
cor_HSIC_vec <- sort(abs(cor_HSIC_mat), decreasing = T)
plot(cor_HSIC_vec)
2-10. Blomqvist’s Beta
library(VineCopula)
cor_blomqvist_mat <- BetaMatrix(gen_dat)
cor_blomqvist_mat[upper.tri(cor_blomqvist_mat, diag = T)] <- NA
cor_blomqvist_mat[1:5,1:5]
## [,1] [,2] [,3] [,4] [,5]
## [1,] NA NA NA NA NA
## [2,] -0.296 NA NA NA NA
## [3,] 0.196 -0.076 NA NA NA
## [4,] 0.016 0.368 -0.276 NA NA
## [5,] 0.692 -0.292 0.224 0.02 NA
cor_blomqvist_vec <- sort(abs(cor_blomqvist_mat), decreasing = T)
plot(cor_blomqvist_vec)
3. Find contrast characteristics among the correlation coefficients above
3-1-1. low pearson (<0.50) and high spearman (>0.5) (linearity vs monotone)
cor_contrast1 <- (abs(cor_pearson_mat) < 0.5) & (abs(cor_spearman_mat) > 0.5)
cor_contrast_ind1 <- which(cor_contrast1, arr.ind = T)
nrow(cor_contrast_ind1)
## [1] 1
3-1-2. Visualization of low pearson (<0.50) and high spearman (>0.5) (linearity vs monotone)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind1)){
index1 <- cor_contrast_ind1[i, 1]; index2 <- cor_contrast_ind1[i, 2]
plot(gen_dat[,index1], gen_dat[,index2], col = gen_label, asp = T,
pch = 16, xlab = paste0(colnames(gen_dat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(gen_dat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3))))
}
3-2-1. high pearson (>0.5) and low spearman (<0.3) (linearity vs monotone)
cor_contrast2 <- (abs(cor_pearson_mat) > 0.5) & (abs(cor_spearman_mat) < 0.3)
cor_contrast_ind2 <- which(cor_contrast2, arr.ind = T)
nrow(cor_contrast_ind2)
## [1] 4
3-2-2. Visualization of high pearson (>0.5) and low spearman (<0.3) (linearity vs monotone)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind2)){
index1 <- cor_contrast_ind2[i, 1]; index2 <- cor_contrast_ind2[i, 2]
plot(gen_dat[,index1], gen_dat[,index2], col = gen_label, asp = T,
pch = 16, xlab = paste0(colnames(gen_dat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(gen_dat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Spearman of ", round(cor_spearman_mat[index1, index2], 3))))
}
3-3-1. high pearson (>0.50) and low distance correlation (<0.40) (linearity vs Non-linearity)
cor_contrast3 <- (abs(cor_pearson_mat) > 0.5) & (abs(cor_dist_mat) < 0.4)
cor_contrast_ind3 <- which(cor_contrast3, arr.ind = T)
nrow(cor_contrast_ind3)
## [1] 6
3-3-2. Visualization of high pearson (>0.70) and low distance correlation (<0.40) (linearity vs Non-linearity)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind3)){
index1 <- cor_contrast_ind3[i, 1]; index2 <- cor_contrast_ind3[i, 2]
plot(gen_dat[,index1], gen_dat[,index2], col = gen_label, asp = T,
pch = 16, xlab = paste0(colnames(gen_dat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(gen_dat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Dist.Cor of ", round(cor_dist_mat[index1, index2], 3))))
}
3-4-1. low pearson (<0.40) and high distance correlation (>0.50) (linearity vs Non-linearity)
cor_contrast4 <- (abs(cor_pearson_mat) < 0.5) & (abs(cor_dist_mat) > 0.5)
cor_contrast_ind4 <- which(cor_contrast4, arr.ind = T)
nrow(cor_contrast_ind4)
## [1] 0
3-7-1. Low pearson (< 0.45) and high XI (> 0.55)
cor_contrast7 <- (abs(cor_pearson_mat) < 0.5) & (abs(cor_XI_mat) > 0.5)
cor_contrast_ind7 <- which(cor_contrast7, arr.ind = T)
nrow(cor_contrast_ind7)
## [1] 0
3-8-1. High Pearson and low XI
cor_contrast8 <- (abs(cor_pearson_mat) > 0.5) & (abs(cor_XI_mat) < 0.5)
cor_contrast_ind8 <- which(cor_contrast8, arr.ind = T)
nrow(cor_contrast_ind8)
## [1] 10
3-8-2. Visualization of high Pearson and low XI
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind8)){
index1 <- cor_contrast_ind8[i, 1]; index2 <- cor_contrast_ind8[i, 2]
plot(gen_dat[,index1], gen_dat[,index2], col = gen_label, asp = T,
pch = 16, xlab = paste0(colnames(gen_dat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(gen_dat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("XI of ", round(cor_XI_mat[index1, index2], 3))))
}
3-9-1. Low Pearson and high Blomqvist’s beta (linearity vs monotone)
cor_contrast9 <- (abs(cor_pearson_mat) < 0.5) & (abs(cor_blomqvist_mat) > 0.5)
cor_contrast_ind9 <- which(cor_contrast9, arr.ind = T)
nrow(cor_contrast_ind9)
## [1] 0
3-10-1. High Pearson (> 0.5) and low Blomqvist’s beta (< 0.1) (linearity vs monotone)
cor_contrast10 <- (abs(cor_pearson_mat) > 0.5) & (abs(cor_blomqvist_mat) < 0.5)
cor_contrast_ind10 <- which(cor_contrast10, arr.ind = T)
nrow(cor_contrast_ind10)
## [1] 6
3-10-2. Visualization of High Pearson (> 0.5) and low Blomqvist’s beta (< 0.1) (linearity vs monotone)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind10)){
index1 <- cor_contrast_ind10[i, 1]; index2 <- cor_contrast_ind10[i, 2]
plot(gen_dat[,index1], gen_dat[,index2], col = gen_label, asp = T,
pch = 16, xlab = paste0(colnames(gen_dat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(gen_dat)[index2], ", (", index2, ")"),
main = paste(paste0("Pearson of ", round(cor_pearson_mat[index1, index2], 3)),
"\n",
paste0("Beta of ", round(cor_blomqvist_mat[index1, index2], 3))))
}
3-11-1. Low kendall and high Distance Correlation (monotone vs non-linearity)
cor_contrast11 <- (abs(cor_kendall_mat) < 0.5) & (abs(cor_dist_mat) > 0.5)
cor_contrast_ind11 <- which(cor_contrast11, arr.ind = T)
nrow(cor_contrast_ind11)
## [1] 0
3-12-1. high kendall and low Distance Correlation (monotone vs non-linearity)
cor_contrast12 <- (abs(cor_kendall_mat) > 0.5) & (abs(cor_dist_mat) < 0.5)
cor_contrast_ind12 <- which(cor_contrast12, arr.ind = T)
nrow(cor_contrast_ind12)
## [1] 2
3-15.1. Low Kendall and high XI
cor_contrast15 <- (abs(cor_kendall_mat) < 0.5) & (abs(cor_XI_mat) > 0.5)
cor_contrast_ind15 <- which(cor_contrast15, arr.ind = T)
nrow(cor_contrast_ind15)
## [1] 0
3-16.1. High Kendall and low XI
cor_contrast16 <- (abs(cor_kendall_mat) > 0.5) & (abs(cor_XI_mat) < 0.5)
cor_contrast_ind16 <- which(cor_contrast16, arr.ind = T)
nrow(cor_contrast_ind16)
## [1] 4
3-16.2. Visualization of high Kendall and low XI
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind16)){
index1 <- cor_contrast_ind16[i, 1]; index2 <- cor_contrast_ind16[i, 2]
plot(gen_dat[,index1], gen_dat[,index2], col = gen_label, asp = T,
pch = 16, xlab = paste0(colnames(gen_dat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(gen_dat)[index2], ", (", index2, ")"),
main = paste(paste0("Kendall of ", round(cor_kendall_mat[index1, index2], 3)),
"\n",
paste0("XI of ", round(cor_XI_mat[index1, index2], 3))))
}
3-17.1. Low distance Correlation and high XI
cor_contrast17 <- (abs(cor_dist_mat) < 0.5) & (abs(cor_XI_mat) > 0.5)
cor_contrast_ind17 <- which(cor_contrast17, arr.ind = T)
nrow(cor_contrast_ind17)
## [1] 0
3-18.1. High distance Correlation and Low XI
cor_contrast18 <- (abs(cor_dist_mat) > 0.5) & (abs(cor_XI_mat) < 0.5)
cor_contrast_ind18 <- which(cor_contrast18, arr.ind = T)
nrow(cor_contrast_ind18)
## [1] 2
3-18.2. Visualization of high distance Correlation and Low XI
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind18)){
index1 <- cor_contrast_ind18[i, 1]; index2 <- cor_contrast_ind18[i, 2]
plot(gen_dat[,index1], gen_dat[,index2], col = gen_label, asp = T,
pch = 16, xlab = paste0(colnames(gen_dat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(gen_dat)[index2], ", (", index2, ")"),
main = paste(paste0("Dist.Cor of ", round(cor_dist_mat[index1, index2], 3)),
"\n",
paste0("XI of ", round(cor_XI_mat[index1, index2], 3))))
}
3-19.1. Low Blomqvist’s Beta and high XI
cor_contrast19 <- (abs(cor_blomqvist_mat) < 0.5) & (abs(cor_XI_mat) > 0.5)
cor_contrast_ind19 <- which(cor_contrast19, arr.ind = T)
nrow(cor_contrast_ind19)
## [1] 0
3-20.1. High Blomqvist’s Beta (> 0.65) and low XI (< 0.45)
cor_contrast20 <- (abs(cor_blomqvist_mat) > 0.65) & (abs(cor_XI_mat) < 0.45)
cor_contrast_ind20 <- which(cor_contrast20, arr.ind = T)
nrow(cor_contrast_ind20)
## [1] 3
3-20.2. Visualization of High Blomqvist’s Beta (> 0.65) and low XI (< 0.45)
par(mfrow = c(2, 5))
for (i in 1:nrow(cor_contrast_ind20)){
index1 <- cor_contrast_ind20[i, 1]; index2 <- cor_contrast_ind20[i, 2]
plot(gen_dat[,index1], gen_dat[,index2], col = gen_label, asp = T,
pch = 16, xlab = paste0(colnames(gen_dat)[index1], ", (", index1, ")"),
ylab = paste0(colnames(gen_dat)[index2], ", (", index2, ")"),
main = paste(paste0("Beta of ", round(cor_blomqvist_mat[index1, index2], 3)),
"\n",
paste0("XI of ", round(cor_XI_mat[index1, index2], 3))))
}
meaning_index <- rbind(cor_contrast_ind1, cor_contrast_ind2, cor_contrast_ind3,
cor_contrast_ind4, cor_contrast_ind5, cor_contrast_ind6,
cor_contrast_ind7, cor_contrast_ind8, cor_contrast_ind9,
cor_contrast_ind10, cor_contrast_ind11, cor_contrast_ind12,
cor_contrast_ind13, cor_contrast_ind14, cor_contrast_ind15,
cor_contrast_ind16, cor_contrast_ind17, cor_contrast_ind18,
cor_contrast_ind19, cor_contrast_ind20)
# c(1,4,6,8)
full_dat1 <- full_dat[, c(1,4,6,8,9)]
save(full_dat1,
file = "full_gen_dat1.RData")
load("full_gen_dat1.RData")
